3.3. Uncertainty in Measurements http://www.ck12.org
when we begin looking at how significant figures are dealt with during calculations. Numbers in many conversion
factors, especially for simple unit conversions, are also exact quantities and have infinite significant figures. There
are exactly 100 centimeters in 1 meter and exactly 60 seconds in 1 minute. Those values are definitions and are not
the result of a measurement.
Sample Problem 3.8: Counting Significant Figures
How many significant figures are there in each of the following measurements?
- 19.5 m
- 0.0051 L
- 204.80 g
- 1.90× 105 s
- 14 beakers
- 700 kg
Step 1: Plan the problem.
Follow the rules for counting the number of significant figures in a measurement, paying special attention to the
location of zeros in each. Note each rule that applies according to the table above (Table3.5).
Step 2: Solve.
- three (rule one)
- two (rule three)
- five (rules two five)
- three (rule five)
- infinite
- one (rule four)
The 14 beakers is a counted set of items and not a measurement, so it has an infinite number of significant figures.
Practice Problems- Count the number of significant figures in each measurement.
a. 0.00090 L
b. 255 baseballs
c. 435,210 m
d. 40.1 kg
e. 9.026× 10 −^6 mm
f. 12.40°C
Significant Figures in Calculations
Many reported quantities in science are the result of calculations involving two or more measurements. Density
involves mass and volume, both of which are measured quantities. As an example, say that you have a precise
balance that gives the mass of a certain object as 21.513 g. However, the volume is measured very roughly by water
displacement, using a graduated cylinder that can only be read to the nearest tenth of a milliliter. The volume of
the object is determined to be 8.2 mL. On a calculator, the density (mass divided by volume) would come out as